I can try. I just read most of the thread and do have some input. I thought you were getting all the advice you needed so I stayed out of it. I'm not the most experienced person with heat tape so I usually leave it for others to comment on.
I think belly heat is better suited for your application. I also think you should include an air space. I don't think air spaces are absolutely necessary but I also like to use them and think it's worth the peace of mind.
Three choices on how to do belly heat with an air space:
1) Cut a hole out of the melamine floor slightly bigger than the size of the tape/connectors/wires you will need. Cover the hole in the floor with scrap expanded PVC (aka PVCX) that you pick up from a sign shop. Your piece of heat tape will fit into this hole, essentialy providing a 3/4" air space. Route a groove or include a thin spacer for the cords to run out. The expanded PVC will conduct heat very nicely.
2) If the species this is for needs a lot of moisture you can cover the entire floor with expanded PVC. Leave the hole as in choice #1.
For examples #1 & 2 you could probably get away with 1/8" thick PVCX.
3) Since your cages are small don't include a melamine floor at all. Simply silicone/staple a piece of PVCX directly to the bottom rim of the cage. This will save weight and make for an easily replacable floor if anything should happen to it. The top of the cage below will support the floor of the cage above.
There is no air space per se in this example but the closed cell nature of the PVCX will conduct heat very much like an air space. PVCX has flame inhibitors and is one material I would not hesitate to sandwich heat tape in. In fact it would probably make it safer.
For this application I would probably go with 1/4" thick PVCX since there is no floor to support it. Also, plan on the connectors and wires haning out of the very back of the cage. Every other part of the heat tape will rest directly on the cage below and the floor itself.
Don't worry too much about not having a melamine floor for the structural integrity. But if you're really uncomfortable with this then go with choice one or two.
I do not like the idea of heat having to conduct all the way through the 3/4" melamine. Given how water resistant PVCX is and how well it conducts heat it's an excellent product for cage floors.
Last comment. If you go with choice 2 or 3 consider tweaking the dimensions of your cages slightly. PVCX is not cheap and you might have a lot less waste if you reduce the length and increase the width (or vice versa) of the cages.
I can help you with this part if you need it.